Scindement d’une équivalence d’homotopie en dimension
Self homotopy equivalences of virtually nilpotent spaces.
Shapes of saturated subsets of compacta
Simply connected coset complexes for rank 1 groups of Lie type.
Some non-trivial PL knots whose complements are homotopy circles
We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.
Some quantitative properties of shapes
Some Topological Properties of Kähler Manifolds and Homogeneous Spaces.
Stratified model categories
The fourth axiom of a model category states that given a commutative square of maps, say i: A → B, g: B → Y, f: A → X, and p: X → Y such that gi = pf, if i is a cofibration, p a fibration and either i or p is a weak equivalence, then a lifting (i.e. a map h: B → X such that ph = g and hi = f) exists. We show that for many model categories the two conditions that either i or p above is a weak equivalence can be embedded in an infinite number of conditions which imply the existence of a lifting (roughly,...
Subdivision yields Alexander duality on independence complexes.
Sur certaines équivalences d'homotopies
On sait qu’il y a 144 classes d’homotopies d’applications de dans lui-même dont la restriction à est homotope à l’identité: ce sont des exemples d’applications qui induisent l’identité en homologie et en homotopie. Plus généralement, soit un complexe de Poincaré 1-connexe de dimension , qui n’a pas le type d’homotopie rationnelle de : si est formel, nous montrons que le groupe des classes d’homotopies d’applications de dans , dont la restriction au -squelette est homotope à l’identité,...
The closure of a model category
The generalized Schoenflies theorem for absolute suspensions
The aim of this paper is to prove the generalized Schoenflies theorem for the class of absolute suspensions. The question whether the finite-dimensional absolute suspensions are homeomorphic to spheres remains open. Partial solution to this question was obtained in [Sz] and [Mi]. Morton Brown gave in [Br] an ingenious proof of the generalized Schoenflies theorem. Careful analysis of his proof reveals that modulo some technical adjustments a similar argument gives an analogous result for the class...
The Group of Homotopy Self-Equivalences of Some Compact CW-Complexes*.
The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²
Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...
The Homotopy Groups of an n-Fold Wedge.
The normalizer of the Weyl group.
The Novikov conjecture and low-dimensional topology.
The relation between homotopy limits and Bauer's shape singular complex
The Stable Topological-hyperbolic Space Form Problem for Complete Manifolds of Finite Volume.
The Suspension of the Loops on a Space with Comultiplication.